1
BITSAT 2023
+3
-1

If the system of linear equation $$3 x-2 y+z=2, 4 x-3 y+3 z=-5$$ and $$7 x-5 y+\lambda z=9$$ has no solution, then $$\lambda$$ equals to

A
4
B
5
C
6
D
7
2
BITSAT 2023
+3
-1

Let $$A=\left[\begin{array}{lll}3 & 2 & 3 \\ 4 & 1 & 0 \\ 2 & 5 & 1\end{array}\right]$$ and $$49 B=\left[\begin{array}{ccc}1 & 13 & -3 \\ -4 & -3 & 12 \\ \alpha & -11 & -5\end{array}\right]$$ If $$B$$ is the inverse of $$A$$, then the value of $$\alpha$$ is

A
0
B
18
C
20
D
5
3
BITSAT 2023
+3
-1

$$\text { If } A=\left[\begin{array}{cc} \sin \theta & -\cos \theta \\ \cos \theta & \sin \theta \end{array}\right] \text {, then } A(\operatorname{adj} A)^{-1} \text { equals to }$$

A
$$\left[\begin{array}{cc} -1 & 0 \\ 0 & -1 \end{array}\right]$$
B
$$\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]$$
C
$$\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]$$
D
$$\left[\begin{array}{cc} 0 & -1 \\ -1 & 0 \end{array}\right]$$
4
BITSAT 2023
+3
-1

If $$a, b, c$$ are non-zero real numbers and if the system of equations $$(a-1) x-y-z=0, -x+(b-1) y-z=0,-x-y+(c-1) z=0$$ has a non-trivial solution, then $$a b+b c+c a$$ equals to

A
$$a b c$$
B
$$a+b+c$$
C
1
D
$$-1$$
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